考虑交易对手违约的单名LCDS定价及其CVA计算

Single name LCDS Pricing and Related CVA Calculation regarding Counterparty Default

摘要:

分析了贷款信用违约互换的主要风险并建立了其定价模型。 在约化框架下，利用单因子反CIR（Cox-Ingersoll-Ross）模型来刻画早偿和违约的负相关性和非负性，并在此假定下得到定价公式的封闭解。 在此基础上考虑了交易对手可违约的单名贷款信用违约互换（LCDS）的信用价值调整（CVA）的计算模型，即在模型中加入LCDS卖方即交易对手的违约强度，并通过一个非线性偏微分方程对模型进行求解。最后，基于CVA计算模型和数值结果，还对错位风险作了讨论。文中的研究表明，考虑交易对手违约的LCDS价格将低于普通LCDS，且价差（CVA）随LCDS合约期限，利率和参考贷款与交易对手违约相关性的增大而增大。考虑交易对手违约的LCDS公平保费率也低于普通LCDS。当参考贷款与交易对手负相关时，CVA的值随负相关程度的增大而减小。

Abstract:

In this paper, under the reduced form framework, a pricing model for loan-only credit default swap (LCDS) with negative correlation between prepayment and default is established. Under reduced framework, by one factor inverse CIR model, we obtain a closed form pricing formula. Using this formula, a calculation scheme for credit value adjustment (CVA) for LCDS is given, where the counterparty risk of the LCDS is considered. Moreover, a wrong way risk related issue is discussed. The research conducted in this article indicates that the price of an LCDS contract with counterparty credit risk (CCR) is lower than one without CCR, and CVA increases with the termination of the LCDS, interest rate and the correlation between the reference loan and the counterparty. The spread for an LCDS with CCR is lower than that of a normal LCDS. If the reference loan is negatively correlated with the counterparty, CVA decreases with the absolute value of the correlation coefficient.